Related papers: A note on Khabibullin's conjecture for integral in…

In the previous paper, we reviewed the Rosenhain's paper to the Jacobi's inversion problem for the genus two hyperelliptic integral. In this paper, we review the G\"{o}pel's paper to the Jacobi's inversion problem for the genus two…

We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.

Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…

This work considers the algebras of functions in the quantum matrix ball. An explicit formula for a positive invariant integral is presented.

This is a survey on Kawaguchi-Silverman conjecture.

We prove a recent conjecture of Hadjicostas concerning a double integral formula involving the zeta and the gamma functions.

We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when…

In this paper, by using hardy inequality, we establish some new integral inequalities of Hardy-Hilbert type with general kernel. As applications, equivalent forms and some particular results are built; the corresponding to the double series…

A complementarity relation is shown between the visibility of interference and bipartite entanglement in a two qubit interferometric system when the parameters of the quantum operation change for a given input state. The entanglement…

This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

We present a conjecture for expressing the coefficients in the Cayley-Hamilton theorem for supermatrices in terms of supertraces. The conjecture is tested for several supermatrix dimensions and unique results are obtained. Generating…

The arithmetic function of two variables is defined. Some properties of the function are given along with the formula that is an analog of the so-called Mobius' inversion formula. A heuristic statement is suggested.

We prove an inequality on positive real numbers, that looks like a reverse to the well-known Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal.

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

In this paper, new refinements for integral and sum forms of H\"older inequality are established. We note that many existing inequalities related to the H\"older inequality can be improved via obtained new inequalities in here, we show this…

In the preprint of 1993 the author formulated some conjectures on monotonicity of ratios for exponential series remainders. They are equivalent to conjectures on monotonicity of a ratio of Kummer hypergeometric functions and presumably not…

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).

We consider two recent conjectures of Harrington, Henninger-Voss, Karhadkar, Robinson and Wong concerning relationships between the sum index, difference index and exclusive sum number of graphs. One conjecture posits an exact relationship…